Adapted variable density subsampling for compressed sensing

Abstract

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most practical application. We try to close this gap by showing how the sparsity patterns can instead be characterised via a probability distribution on the supports of the sparse signals allowing us to again derive optimal subsampling strategies. This probability distribution can be easily estimated from signals of the same signal class, achieving state of the art performance in numerical experiments. Our approach also extends to structured acquisition, where instead of isolated measurements, blocks of measurements are taken.